Previous Refusal on Good Character

I am seeking advice on behalf of someone who is considering applying for naturalisation as a British citizen but is concerned about a past issue with the Home Office.

In 2011, the individual applied for naturalisation, but the application was refused due to inconsistencies in identity information. The Home Office identified a fingerprint match linking the person to a record of someone removed from the UK in 2002 under a different name and date of birth. In the application, the individual had claimed to be of a different country origin and stated they entered the UK in 2005 under another identity.

The Home Office concluded that the individual had not been open and honest in their dealings, and therefore, they did not meet the "good character" requirement at the time. The refusal letter also indicated that this matter would be taken into account for assessing good character for a period of 10 years from the date of the letter (2011).

Since then, the individual has lived continuously in the UK, complied fully with the law, and has not had any further immigration issues.

Now that more than 10 years have passed since the refusal, will this matter still affect their chances of being approved for naturalisation now if they continue to deny the claim from the Home Office.

Thank you in advance for any insights or guidance.